When Mathematicians and AI Join Forces: The Quest to Solve Math's Toughest Puzzles
The Mathematics of High Stakes
There's something almost romantic about the culture of mathematical problem-solving. Mathematicians don't just stumble upon these conjectures—they hunt them, obsess over them, and occasionally win Fields Medals for solving them. The longer a problem resists proof, the more prestigious its eventual solution becomes.
In June, something remarkable happened. Groups from London to Berkeley convened to compile a new list of 50 problems with an important constraint: every problem must be verifiable by automated checking. This isn't just academic neatness—it bridges the gap between human intuition and machine verification, creating a framework where AI and mathematicians can truly collaborate.
Yang-Hui He, a mathematician at the London Institute for Mathematical Sciences, brought his young son to one workshop. Under the watchful eye of a cake-munching child, mathematicians collaborated to submit problems spanning knot theory, algebra, topology, and number theory. There's something wonderfully human about that image—centuries-old mathematical tradition meeting the next generation.
The Problems That Keep Mathematicians Up at Night
The list reads like a greatest-hits collection of mathematical suffering. Here are a few that stood out:
The Sum of Three Cubes
What happens when you try to express a number as the sum of three cubes? The equation x³ + y³ + z³ = k has perplexed mathematicians for decades. In 2020, Andrew Booker and Andrew Sutherland solved the case for k=42, consuming 1.3 million computing hours across volunteer home computers. The next target? 114. The catch? The smallest solutions likely have around 30 digits—solving it with brute force could cost $100 million or more.
The Apéry-Style Irrationality Proof
Irrational numbers—decimals that can't be expressed as clean fractions—hide deep secrets. While pi and √2 are familiar examples, proving irrationality is notoriously difficult. It took two millennia to prove pi was irrational. In 1978, Roger Apéry proved that ζ(3) (the sum of 1/n³) was irrational using a mysterious "sandwiching" technique. When asked how he found his proof, Apéry reportedly said he found it in a flower pot. That mystery remains unsolved to this day.
The Lonely Runner Conjecture
Here's a problem that sounds almost whimsical: place runners on a circular track, each running at a unique constant speed. The conjecture predicts that at some point, each runner will be maximally distant from all others—their "loneliest" moment. Simple to state, devilishly difficult to prove.
AI Enters the Fray
The most fascinating aspect of this project is its connection to artificial intelligence. Epoch AI commissioned the list specifically to benchmark AI progress. And the timing is curious—OpenAI recently claimed a solution to the Navier-Stokes problem, one of the seven Millennium Prize Problems worth $1 million each.
As of late September, a few problems from the new list have been solved, though the official collection still brims with challenges. OpenAI has announced that its unreleased internal AI model has solved more than 100 open questions, though how many of those are on this specific list remains unclear.
Why This Matters for the Tech World
You might be wondering what centuries-old mathematical conjectures have to do with modern software development or cloud hosting. More than you think.
First, mathematical problem-solving drives computational innovation. The brute-force approach to solving "sum of three cubes" for k=42 required distributed computing across thousands of volunteer machines—a preview of modern cloud infrastructure.
Second, the intersection of AI and formal verification touches every aspect of software reliability. When mathematicians insist problems be "automatically checkable," they're practicing what software engineers call formal methods—the same principles that make secure systems trustworthy.
Third, and perhaps most importantly, the spirit of tackling impossible problems is exactly what drives technological innovation. Whether you're solving the Riemann Hypothesis or building the next scalable hosting platform, the approach is similar: identify the constraints, find elegant solutions, and verify your work.
The mathematical community's collaboration with AI organizations represents a new chapter in discovery. These 50 problems aren't just academic curiosities—they're benchmarks for human-AI partnership in intellectual pursuit. And in an era where we're building AI-assisted development tools and vibe coding platforms, watching AI tackle mathematics' toughest challenges gives us a glimpse of the future we're building.
The flower pot mystery remains unsolved. But somewhere, an AI might be getting closer to understanding how Apéry found his proof.